Atkin-Lehner |
2- 7- 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
54782bi |
Isogeny class |
Conductor |
54782 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
470016 |
Modular degree for the optimal curve |
Δ |
-5947887355691008 = -1 · 224 · 73 · 13 · 433 |
Discriminant |
Eigenvalues |
2- -2 -2 7- -5 13+ -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,38016,2375680] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:688:1] [-24:1216:1] |
Generators of the group modulo torsion |
j |
17714468849401241/17340779462656 |
j-invariant |
L |
8.9754712797487 |
L(r)(E,1)/r! |
Ω |
0.27991609688936 |
Real period |
R |
0.22267265926318 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54782bq1 |
Quadratic twists by: -7 |